Question: Determine the value of $x$ that satisfies $\sqrt[5]{x\sqrt{x^3}}=3$.
Answer: We can first rewrite the term under the fifth root: $x\sqrt{x^3} = x \cdot x^{3/2} = x^{5/2}$. Then we simplify the entire expression on the left side of the equation, which gives  $\sqrt[5]{x^{5/2}}=(x^{5/2})^{1/5} = x ^{(5/2)\cdot(1/5)} = x^{1/2}$. We now have $\sqrt{x}=3$ and we can square each side to find $x=\boxed{9}$.